Deformation quantisation for unshifted symplectic structures on derived Artin stacks

摘要

We construct a map from DQ algebroid quantisations of unshifted symplecticstructures on a derived Artin N-stack to power series in de Rham cohomology,depending only on a choice of Levi decomposition for theGrothendieck--Teichmueller group. This gives an equivalence between even powerseries and certain involutive quantisations, which yield involutive curvedA-infinity deformations of the dg category of perfect complexes. In particular,there is a canonical quantisation associated to every symplectic structure onsuch a stack, which agrees for smooth varieties with the Kontsevich--Tamarkinquantisation.